Abstract
Based upon the nonlinear model of random sea waves, the statistical distribution of wave surface elevation exact to the fourth order is derived as the truncated Gram-Charlier series,by calculating directly each order moment. The phenomenon found by Huanget al. that the agreement between observed data and investigated series deteriorates much more when the series is kept to λ8 is explained. The effect of the approximation order on the truncation of series and the determination of coefficients is investigated. For themth order approximation, the derived series is truncated atH3m-3 with the absence of H3m-4, and the coefficients ofH3m-3 andH3m-6 are connected by a simple algebraic relation.
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